Potential energy functions of the MgH molecule are investigated by the MRCI method using large active space and basis sets. The calculations are performed up to the Mg(3s3d, 1D) + H dissociation limit. The molecular constants compare well with the available data. The dipole moment functions exhibit a series of crossings due to the strong interactions between the states. Radial and rotational couplings among these states are also calculated, with a state-averaged MCSCF approach. This work will enable calculations of collisional cross sections and rate coefficients, important for the modelling of stellar spectra when collisions compete with radiative processes in non-LTE conditions. (C) 2010 Elsevier B. V. All rights reserved.